Mathematical Sciences: Research in Circle Packings, Quasiconformal Geometry and Complex Function Theory

首席研究员将研究圆填充和拟共形映射。本文研究的一个主要问题是Koeba均匀化猜想，即扩展复平面上的任何区域都与扩展平面上的圆区域共形同胚。本研究中使用的技术与拟共形映射理论密切相关。该奖项将支持微分几何和全局分析领域的研究。微分几何是研究空间几何与空间上定义的解析概念之间关系的学科。全局分析是通过拼凑局部信息来研究空间的整体几何和拓扑特性。这些数学领域在其他科学中的应用包括复杂分子的结构、液气边界和宇宙的大尺度结构。

The principal investigator will study circle packings and quasiconformal mappings. One main problem to be studied is the Koeba uniformization conjecture which states that any domain in the extended complex plane is conformally homeomorphic to a circle domain in the extended plane. The techniques to be used in this study are closely related to the theory of quasiconformal maps. This award will support research in the general area of differential geometry and global analysis. Differential geometry is the study of the relationship between the geometry of a space and analytic concepts defined on the space. Global analysis is the study of the overall geometric and topological properties of a space by piecing together local information. Applications of these areas of mathematics in other sciences include the structure of complicated molecules, liquid-gas boundaries, and the large scale structure of the universe.